Advertisement

Vehicle Routing with Stochastic Demands: Models & Computational Methods

  • Moshe Dror
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 46)

Abstract

In this paper we provide an overview and modeling details regarding vehicle routing in situations in which customer demand is revealed only when the vehicle arrives at the customer’s location. Given a fixed capacity vehicle, this setting gives rise to the possibility that the vehicle on arrival does not have sufficient inventory to completely supply a given customer’s demand. Such an occurrence is called a route failure and it requires additional vehicle trips to fully replenish such a customer. Given a set of customers, the objective is to design vehicle routes and response policies which minimize the expected delivery cost by a fleet of fixed capacity vehicles. We survey the different problem statements and formulations. In addition, we describe a number of the algorithmic developments for constructing routing solutions. Primarily we focus on stochastic programming models with different recourse options. We also present a Markov decision approach for this problem and conclude with a cha llenging conjecture regarding finite sums of random variables.

Keywords

Travel Salesman Problem Travel Salesman Problem Vehicle Route Stochastic Demand Route Failure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Applegate, D., R. Bixby, V. Chvatal, and W. Cook. (1998). “On the solution of traveling salesman problem”, Documenta Mathemaitica, extra volume ICM 1998; III, 645–656.MathSciNetzbMATHGoogle Scholar
  2. Bertsimas, D.J. (1992). “A vehicle routing problem with stochastic demand”, Operations Research 40, 574–585.MathSciNetCrossRefGoogle Scholar
  3. Bertsimas, D.J., P. Chevi, and M. Peterson. (1995). “Computational approaches to stochastic vehicle routing problems”, Transportation Science 29,342–352.CrossRefGoogle Scholar
  4. Birge, J.R. (1985). “decomposition and partition methods for multistage stochastic linear programs”, Operations Research 33, 989–1007.MathSciNetCrossRefGoogle Scholar
  5. Clarke, C. and J.W. Wright. (1964). “Scheduling of vehicles from a central depot to a number of delivery points”, Operations Research 12, 568–581.CrossRefGoogle Scholar
  6. Dror, M. (1983). The Inventory Routing Problem, Ph.D. Thesis, University of Maryland. College Park, Maryland, USA.Google Scholar
  7. Dror, M. (1993). “Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution”, European J. of Operational Research 64, 532–441.CrossRefGoogle Scholar
  8. Dror, M. and P. Trudeau. (1986). “Stochastic vehicle routing with modified savings algorithm”, European Journal of Operations Research 23, 228–235.MathSciNetCrossRefGoogle Scholar
  9. Dror, M, M.O. Ball, and B.L. Golden. (1985). “Computational comparison of algorithms for inventory routing”, Annals of Operations Research 4, 3–23.MathSciNetCrossRefGoogle Scholar
  10. Dror, M., G. Laporte, and P. Trudeau. (1989). “Vehicle routing with stochastic demands: Properties and solution framework”, Transportation Science 23, 166–176.MathSciNetCrossRefGoogle Scholar
  11. Dror, M., G. Laporte, and V.F. Louveaux. (1993). “Vehicle routing with stochastic demands and restricted failures”, ZOR-Zeitschrift fur Operations Research 37, 273–283.MathSciNetzbMATHGoogle Scholar
  12. Eilon, S, C.D.T. Watson-Gandy, N. Christofides. (1971). Distribution Management: Mathematical Modelling and Practical Analysis, Griffin, London.Google Scholar
  13. Jailet, P. (1985). “Probabilistic traveling salesman problem”, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.Google Scholar
  14. Kreimer J. and M. Dror. (1990). “The monotonicity of the threshold detection probability in stochastic accumulation process”, Computers & Operations Research 17, 63–71.MathSciNetCrossRefGoogle Scholar
  15. Laipala, T. (1978). “On the solutions of the stochastic traveling salesman problems”, European J. of Operational Research 2, 291–297.MathSciNetCrossRefGoogle Scholar
  16. Laporte, G. and F.V. Louveaux. (1993). “The integer L-shaped method for stochastic integer programs with complete recourse”, Operations Research Letters 13, 133–142.MathSciNetCrossRefGoogle Scholar
  17. Laporte, G., F.V. Louveaux, and L. Van hamme. (2001). “An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands”, Operations Research (forthcoming).Google Scholar
  18. Larson, R.C. (1988). “Transportation of sludge to the 106-mile site: An inventory routing algorithm for fleet sizing and logistical system design”, Transportation Science 22, 186–198.CrossRefGoogle Scholar
  19. Noon, C.E. and J.C. Bean. (1991). “A Lagrnagian based approach to the asymmetric Generalized Traveling Salesman Problem”, Operations Research 39, 623–632.MathSciNetCrossRefGoogle Scholar
  20. Noon, C.E. and J.C. Bean. (1993). “An efficient transformation of the Generalized Traveling Salesman Problem”, IN FOR 31, 39–44.zbMATHGoogle Scholar
  21. Secomandi, N. (1998). “Exact and Heuristic Dynamic Programming Algorithms for the Vehicle Routing Problem with Stcochastic Demands”, Doctoral Dissertation, University of Houston, USA.Google Scholar
  22. Secomandi, N. (2000). “Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands”, Computers & Operations Research 27, 1201–1225.CrossRefGoogle Scholar
  23. Stewart, W.R., Jr. and B.L. Golden. (1983). “Stochastic vehicle routing: A comprehensive approach”, European Journal of Operational Research 14, 371–385.CrossRefGoogle Scholar
  24. Stewart, W.R., Jr., B.L. Golden, and F. Gheysens. (1983). “A survey of stochastic vehicle routing”, Working Paper MS/S, College of Business and Management, University of Maryland at College Park.Google Scholar
  25. Trudeau, P. and M. Dror. (1992). “Stochastic inventory routing: Stockouts and route failure”, Transportation Science 26,172–184.CrossRefGoogle Scholar
  26. Yang, W.-H. (1996). “Stochastic Vehicle Routing with Optimal Restocking”, Ph.D. Thesis, Case Western Reserve University, Cleveland, OH.Google Scholar
  27. Yang, W.-H., K. Mathur, and R.H. Ballou. (2000). “Stochastic vehicle routing problem with restocking”, Transportation Science 34, 99–112.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2002

Authors and Affiliations

  • Moshe Dror
    • 1
  1. 1.Department of Management Information SystemsThe University of ArizonaTucsonUSA

Personalised recommendations